%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV066^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:12 AM UTC 2026
% Result : Theorem 1.66s 1.38s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 861 ( 328 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 1068 ( 61 ~; 147 |; 38 &; 814 @)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 554 ( 554 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 753 ( 594 ^; 125 !; 34 ?; 753 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_5,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_6,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_8,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_9,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_11,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK9: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_19,type,
sK10: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(f430,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f82,f429]) ).
thf(f429,plain,
spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f428]) ).
thf(f428,plain,
( $false
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f424,f44]) ).
thf(f44,plain,
( ( ( ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i] : $true ) )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl6_2
<=> ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f424,plain,
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ( $true != $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| spl6_2 ),
inference(boolean_simplification,[status(thm)],[f421]) ).
thf(f421,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $true != $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| spl6_2 ),
inference(boolean_simplification,[status(thm)],[f419]) ).
thf(f419,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f418]) ).
thf(f418,plain,
( ( $false = $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f405]) ).
thf(f405,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X0 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X0 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true ) )
| spl6_2 ),
inference(superposition,[status(thm)],[f16,f312]) ).
thf(f312,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f311]) ).
thf(f311,plain,
( ( $false = $true )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(duplicate_literal_removal,[status(thm)],[f310]) ).
thf(f310,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $false = $true )
| ( $false = $true )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f293]) ).
thf(f293,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X1 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X0 )
= $true ) )
| spl6_2 ),
inference(superposition,[status(thm)],[f189,f273]) ).
thf(f273,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $false = $true )
| spl6_2 ),
inference(duplicate_literal_removal,[status(thm)],[f271]) ).
thf(f271,plain,
( ( $false = $true )
| ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $false = $true )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,plain,
( ! [X10: $i,X9: $i] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(primitive_instantiation,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f152,f44]) ).
thf(f152,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( ( ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( $true != $true )
| ( ( ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( X1
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X9 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X10: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X9: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true )
| ( ( X1 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true ) )
| ( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true )
& ! [X8: $i] :
( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true ) )
& ! [X9: $i] :
( ( ( X1 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true ) ) )
| ! [X10: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i,X3: $i > $o] :
( ( ( X1 @ X3 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X3 @ X2 )
!= $true ) )
=> ( ( ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ? [X7: $i] :
( ( ( X0 @ X4 @ X5 @ X7 )
!= $true )
& ( ( X1 @ X4 @ X5 @ X7 )
!= $true ) )
& ! [X8: $i] :
( ( ( X0 @ X4 @ X6 @ X8 )
= $true )
| ( ( X1 @ X4 @ X6 @ X8 )
= $true ) )
& ! [X9: $i] :
( ( ( X1 @ X6 @ X5 @ X9 )
= $true )
| ( ( X0 @ X6 @ X5 @ X9 )
= $true ) ) )
=> ( ? [X7: $i] :
( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
!= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
!= $true ) )
& ! [X8: $i] :
( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true ) )
& ! [X9: $i] :
( ( ( X1 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true )
| ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X9 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X7: $i] :
( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
!= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
!= $true ) )
=> ( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i,X3: $i > $o] :
( ( ( X1 @ X3 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X3 @ X2 )
!= $true ) )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ? [X7: $i] :
( ( ( X0 @ X4 @ X5 @ X7 )
!= $true )
& ( ( X1 @ X4 @ X5 @ X7 )
!= $true ) )
& ! [X8: $i] :
( ( ( X0 @ X4 @ X6 @ X8 )
= $true )
| ( ( X1 @ X4 @ X6 @ X8 )
= $true ) )
& ! [X9: $i] :
( ( ( X1 @ X6 @ X5 @ X9 )
= $true )
| ( ( X0 @ X6 @ X5 @ X9 )
= $true ) ) )
| ! [X10: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i,X2: $i > $o] :
( ( ( X0 @ X2 @ X2 @ X3 )
!= $true )
& ( ( X1 @ X2 @ X2 @ X3 )
!= $true ) )
| ? [X5: $i > $o,X6: $i > $o,X4: $i > $o] :
( ? [X9: $i] :
( ( ( X1 @ X5 @ X6 @ X9 )
!= $true )
& ( ( X0 @ X5 @ X6 @ X9 )
!= $true ) )
& ! [X7: $i] :
( ( ( X1 @ X5 @ X4 @ X7 )
= $true )
| ( ( X0 @ X5 @ X4 @ X7 )
= $true ) )
& ! [X8: $i] :
( ( ( X0 @ X4 @ X6 @ X8 )
= $true )
| ( ( X1 @ X4 @ X6 @ X8 )
= $true ) ) )
| ! [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ? [X9: $i] :
( ( ( X1 @ X5 @ X6 @ X9 )
!= $true )
& ( ( X0 @ X5 @ X6 @ X9 )
!= $true ) )
& ! [X8: $i] :
( ( ( X0 @ X4 @ X6 @ X8 )
= $true )
| ( ( X1 @ X4 @ X6 @ X8 )
= $true ) )
& ! [X7: $i] :
( ( ( X1 @ X5 @ X4 @ X7 )
= $true )
| ( ( X0 @ X5 @ X4 @ X7 )
= $true ) ) )
| ? [X3: $i,X2: $i > $o] :
( ( ( X0 @ X2 @ X2 @ X3 )
!= $true )
& ( ( X1 @ X2 @ X2 @ X3 )
!= $true ) )
| ! [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ! [X8: $i] :
( ( ( X0 @ X4 @ X6 @ X8 )
= $true )
| ( ( X1 @ X4 @ X6 @ X8 )
= $true ) )
& ! [X7: $i] :
( ( ( X1 @ X5 @ X4 @ X7 )
= $true )
| ( ( X0 @ X5 @ X4 @ X7 )
= $true ) ) )
=> ! [X9: $i] :
( ( ( X1 @ X5 @ X6 @ X9 )
= $true )
| ( ( X0 @ X5 @ X6 @ X9 )
= $true ) ) )
& ! [X2: $i > $o,X3: $i] :
( ( ( X0 @ X2 @ X2 @ X3 )
= $true )
| ( ( X1 @ X2 @ X2 @ X3 )
= $true ) )
& ~ ! [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i] :
( ( X0 @ X2 @ X2 @ X3 )
| ( X1 @ X2 @ X2 @ X3 ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X7: $i] :
( ( X1 @ X5 @ X4 @ X7 )
| ( X0 @ X5 @ X4 @ X7 ) )
& ! [X8: $i] :
( ( X1 @ X4 @ X6 @ X8 )
| ( X0 @ X4 @ X6 @ X8 ) ) )
=> ! [X9: $i] :
( ( X1 @ X5 @ X6 @ X9 )
| ( X0 @ X5 @ X6 @ X9 ) ) )
& ~ ! [X10: $i] :
( ( X0
@ ^ [X11: $i] : $true
@ ^ [X12: $i] : $false
@ X10 )
| ( X1
@ ^ [X13: $i] : $true
@ ^ [X14: $i] : $false
@ X10 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i] :
( ( X1 @ X2 @ X2 @ X3 )
| ( X0 @ X2 @ X2 @ X3 ) )
& ! [X4: $i > $o,X2: $i > $o,X5: $i > $o] :
( ( ! [X3: $i] :
( ( X0 @ X2 @ X4 @ X3 )
| ( X1 @ X2 @ X4 @ X3 ) )
& ! [X3: $i] :
( ( X0 @ X4 @ X5 @ X3 )
| ( X1 @ X4 @ X5 @ X3 ) ) )
=> ! [X3: $i] :
( ( X0 @ X2 @ X5 @ X3 )
| ( X1 @ X2 @ X5 @ X3 ) ) )
& ~ ! [X3: $i] :
( ( X1
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : $false
@ X3 )
| ( X0
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : $false
@ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i] :
( ( X1 @ X2 @ X2 @ X3 )
| ( X0 @ X2 @ X2 @ X3 ) )
& ! [X4: $i > $o,X2: $i > $o,X5: $i > $o] :
( ( ! [X3: $i] :
( ( X0 @ X2 @ X4 @ X3 )
| ( X1 @ X2 @ X4 @ X3 ) )
& ! [X3: $i] :
( ( X0 @ X4 @ X5 @ X3 )
| ( X1 @ X4 @ X5 @ X3 ) ) )
=> ! [X3: $i] :
( ( X0 @ X2 @ X5 @ X3 )
| ( X1 @ X2 @ X5 @ X3 ) ) )
& ~ ! [X3: $i] :
( ( X1
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : $false
@ X3 )
| ( X0
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : $false
@ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fALW8lDNi7/DTF2THF_21395.p',cTHM120D_pme) ).
thf(f189,plain,
( ! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f182,f44]) ).
thf(f182,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( $true != $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X10: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X10: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f16,plain,
! [X10: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 )
= $true )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f82,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false = $true )
| ~ spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl6_2 ),
inference(argument_congruence,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV066^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:40:06 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV066^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory (Relations)
% 0.31/0.46 % Problem : TPS problem THM120D
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0439 [Bro09]
% 0.31/0.46 % : THM120D [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.42 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.55 v8.1.0, 0.75 v7.4.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.57 v6.3.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 40 ( 1 ~; 5 |; 3 &; 30 @)
% 0.31/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 15 ( 15 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 0 usr; 2 con; 0-0 aty)
% 0.31/0.46 % Number of variables : 15 ( 4 ^; 9 !; 2 ?; 15 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(cTHM120D_pme,conjecture,
% 0.31/0.46 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 0.31/0.46 ( ! [Xx: $i > $o,Xw_2: $i] :
% 0.31/0.46 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 0.31/0.46 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 0.31/0.46 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.31/0.46 ( ( ! [Xw_2: $i] :
% 0.31/0.46 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 0.31/0.46 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 0.31/0.46 & ! [Xw_2: $i] :
% 0.31/0.46 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 0.31/0.46 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 0.31/0.46 => ! [Xw_2: $i] :
% 0.31/0.46 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 0.31/0.46 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 0.31/0.46 & ~ ! [Xw_2: $i] :
% 0.31/0.46 ( ( Xr_27
% 0.31/0.46 @ ^ [Xx: $i] : $true
% 0.31/0.46 @ ^ [Xx: $i] : $false
% 0.31/0.46 @ Xw_2 )
% 0.31/0.46 | ( Xr_28
% 0.31/0.46 @ ^ [Xx: $i] : $true
% 0.31/0.46 @ ^ [Xx: $i] : $false
% 0.31/0.46 @ Xw_2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 12:40:07 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fALW8lDNi7/DTF2DTF21395.p
% See solution above
% 1.46/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(cTHM120D_pme,conjecture,
% 1.66/1.30 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 1.66/1.30 ( ! [Xx: $i > $o,Xw_2: $i] :
% 1.66/1.30 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 1.66/1.30 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 1.66/1.30 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.66/1.30 ( ( ! [Xw_2: $i] :
% 1.66/1.30 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 1.66/1.30 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 1.66/1.30 & ! [Xw_2: $i] :
% 1.66/1.30 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 1.66/1.30 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 1.66/1.30 => ! [Xw_2: $i] :
% 1.66/1.30 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 1.66/1.30 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 1.66/1.30 & ~ ! [Xw_2: $i] :
% 1.66/1.30 ( ( Xr_27
% 1.66/1.30 @ ^ [Xx: $i] : $true
% 1.66/1.30 @ ^ [Xx: $i] : $false
% 1.66/1.30 @ Xw_2 )
% 1.66/1.30 | ( Xr_28
% 1.66/1.30 @ ^ [Xx: $i] : $true
% 1.66/1.30 @ ^ [Xx: $i] : $false
% 1.66/1.30 @ Xw_2 ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.32 % (21669)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/2Mi)
% 1.66/1.32 % (21667)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/4Mi)
% 1.66/1.32 % (21669)Instruction limit reached!
% 1.66/1.32 % (21669)------------------------------
% 1.66/1.32 % (21669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (21669)Termination reason: Unknown
% 1.66/1.32 % (21669)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (21669)Memory used [KB]: 1023
% 1.66/1.32 % (21669)Time elapsed: 0.002 s
% 1.66/1.32 % (21669)Instructions burned: 3 (million)
% 1.66/1.32 % (21669)------------------------------
% 1.66/1.32 % (21669)------------------------------
% 1.66/1.32 % (21667)Instruction limit reached!
% 1.66/1.32 % (21667)------------------------------
% 1.66/1.32 % (21667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (21667)Termination reason: Unknown
% 1.66/1.32 % (21667)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (21667)Memory used [KB]: 5500
% 1.66/1.32 % (21667)Time elapsed: 0.003 s
% 1.66/1.32 % (21667)Instructions burned: 6 (million)
% 1.66/1.32 % (21667)------------------------------
% 1.66/1.32 % (21667)------------------------------
% 1.66/1.32 % (21666)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/183Mi)
% 1.66/1.32 % (21668)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/27Mi)
% 1.66/1.32 % (21670)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/2Mi)
% 1.66/1.32 % (21672)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/18Mi)
% 1.66/1.32 % (21671)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/275Mi)
% 1.66/1.33 % (21670)Instruction limit reached!
% 1.66/1.33 % (21670)------------------------------
% 1.66/1.33 % (21670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (21670)Termination reason: Unknown
% 1.66/1.33 % (21670)Termination phase: Property scanning
% 1.66/1.33
% 1.66/1.33 % (21670)Memory used [KB]: 895
% 1.66/1.33 % (21670)Time elapsed: 0.003 s
% 1.66/1.33 % (21670)Instructions burned: 2 (million)
% 1.66/1.33 % (21670)------------------------------
% 1.66/1.33 % (21670)------------------------------
% 1.66/1.33 % (21673)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/3Mi)
% 1.66/1.33 % (21673)Instruction limit reached!
% 1.66/1.33 % (21673)------------------------------
% 1.66/1.33 % (21673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (21673)Termination reason: Unknown
% 1.66/1.33 % (21673)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (21673)Memory used [KB]: 1023
% 1.66/1.33 % (21673)Time elapsed: 0.002 s
% 1.66/1.33 % (21673)Instructions burned: 4 (million)
% 1.66/1.33 % (21673)------------------------------
% 1.66/1.33 % (21673)------------------------------
% 1.66/1.33 % (21674)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/37Mi)
% 1.66/1.33 % (21668)Refutation not found, incomplete strategy
% 1.66/1.33 % (21668)------------------------------
% 1.66/1.33 % (21668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (21668)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (21668)Memory used [KB]: 5500
% 1.66/1.33 % (21668)Time elapsed: 0.007 s
% 1.66/1.33 % (21668)Instructions burned: 8 (million)
% 1.66/1.33 % (21668)------------------------------
% 1.66/1.33 % (21668)------------------------------
% 1.66/1.34 % (21672)Instruction limit reached!
% 1.66/1.34 % (21672)------------------------------
% 1.66/1.34 % (21672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (21672)Termination reason: Unknown
% 1.66/1.34 % (21672)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (21672)Memory used [KB]: 5628
% 1.66/1.34 % (21672)Time elapsed: 0.013 s
% 1.66/1.34 % (21672)Instructions burned: 19 (million)
% 1.66/1.34 % (21672)------------------------------
% 1.66/1.34 % (21672)------------------------------
% 1.66/1.34 % (21676)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/3Mi)
% 1.66/1.34 % (21676)Instruction limit reached!
% 1.66/1.34 % (21676)------------------------------
% 1.66/1.34 % (21676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (21676)Termination reason: Unknown
% 1.66/1.34 % (21676)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (21676)Memory used [KB]: 1023
% 1.66/1.34 % (21676)Time elapsed: 0.002 s
% 1.66/1.34 % (21676)Instructions burned: 4 (million)
% 1.66/1.34 % (21676)------------------------------
% 1.66/1.34 % (21676)------------------------------
% 1.66/1.34 % (21674)Instruction limit reached!
% 1.66/1.34 % (21674)------------------------------
% 1.66/1.34 % (21674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (21674)Termination reason: Unknown
% 1.66/1.34 % (21674)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (21674)Memory used [KB]: 5884
% 1.66/1.34 % (21674)Time elapsed: 0.014 s
% 1.66/1.34 % (21674)Instructions burned: 40 (million)
% 1.66/1.34 % (21674)------------------------------
% 1.66/1.34 % (21674)------------------------------
% 1.66/1.34 % (21675)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/15Mi)
% 1.66/1.35 % (21679)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/16Mi)
% 1.66/1.35 % (21677)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/1041Mi)
% 1.66/1.35 % (21680)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/3Mi)
% 1.66/1.35 % (21675)Instruction limit reached!
% 1.66/1.35 % (21675)------------------------------
% 1.66/1.35 % (21675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (21675)Termination reason: Unknown
% 1.66/1.35 % (21675)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (21675)Memory used [KB]: 5628
% 1.66/1.35 % (21675)Time elapsed: 0.011 s
% 1.66/1.35 % (21675)Instructions burned: 15 (million)
% 1.66/1.35 % (21675)------------------------------
% 1.66/1.35 % (21675)------------------------------
% 1.66/1.35 % (21679)Instruction limit reached!
% 1.66/1.35 % (21679)------------------------------
% 1.66/1.35 % (21679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (21679)Termination reason: Unknown
% 1.66/1.35 % (21679)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (21679)Memory used [KB]: 5628
% 1.66/1.35 % (21679)Time elapsed: 0.006 s
% 1.66/1.35 % (21679)Instructions burned: 17 (million)
% 1.66/1.35 % (21679)------------------------------
% 1.66/1.35 % (21679)------------------------------
% 1.66/1.35 % (21680)Instruction limit reached!
% 1.66/1.35 % (21680)------------------------------
% 1.66/1.35 % (21680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (21680)Termination reason: Unknown
% 1.66/1.35 % (21680)Termination phase: Twee Goal Transformation
% 1.66/1.35
% 1.66/1.35 % (21680)Memory used [KB]: 1023
% 1.66/1.35 % (21680)Time elapsed: 0.003 s
% 1.66/1.35 % (21680)Instructions burned: 4 (million)
% 1.66/1.35 % (21680)------------------------------
% 1.66/1.35 % (21680)------------------------------
% 1.66/1.35 % (21678)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/7Mi)
% 1.66/1.36 % (21678)Instruction limit reached!
% 1.66/1.36 % (21678)------------------------------
% 1.66/1.36 % (21678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (21678)Termination reason: Unknown
% 1.66/1.36 % (21678)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (21678)Memory used [KB]: 1023
% 1.66/1.36 % (21678)Time elapsed: 0.006 s
% 1.66/1.36 % (21678)Instructions burned: 7 (million)
% 1.66/1.36 % (21678)------------------------------
% 1.66/1.36 % (21678)------------------------------
% 1.66/1.36 % (21682)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/7Mi)
% 1.66/1.36 % (21682)Instruction limit reached!
% 1.66/1.36 % (21682)------------------------------
% 1.66/1.36 % (21682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (21682)Termination reason: Unknown
% 1.66/1.36 % (21682)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (21682)Memory used [KB]: 5500
% 1.66/1.36 % (21682)Time elapsed: 0.003 s
% 1.66/1.36 % (21682)Instructions burned: 7 (million)
% 1.66/1.36 % (21682)------------------------------
% 1.66/1.36 % (21682)------------------------------
% 1.66/1.37 % (21681)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/3Mi)
% 1.66/1.37 % (21683)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/3Mi)
% 1.66/1.37 % (21681)Instruction limit reached!
% 1.66/1.37 % (21681)------------------------------
% 1.66/1.37 % (21681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (21681)Termination reason: Unknown
% 1.66/1.37 % (21681)Termination phase: shuffling
% 1.66/1.37
% 1.66/1.37 % (21681)Memory used [KB]: 1023
% 1.66/1.37 % (21681)Time elapsed: 0.004 s
% 1.66/1.37 % (21681)Instructions burned: 4 (million)
% 1.66/1.37 % (21681)------------------------------
% 1.66/1.37 % (21681)------------------------------
% 1.66/1.37 % (21683)Instruction limit reached!
% 1.66/1.37 % (21683)------------------------------
% 1.66/1.37 % (21683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (21683)Termination reason: Unknown
% 1.66/1.37 % (21683)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (21683)Memory used [KB]: 5500
% 1.66/1.37 % (21683)Time elapsed: 0.004 s
% 1.66/1.37 % (21683)Instructions burned: 3 (million)
% 1.66/1.37 % (21683)------------------------------
% 1.66/1.37 % (21683)------------------------------
% 1.66/1.37 % (21685)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/18Mi)
% 1.66/1.37 % (21684)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21395 for (2999ds/4Mi)
% 1.66/1.37 % (21671)First to succeed.
% 1.66/1.38 % (21685)Refutation not found, incomplete strategy
% 1.66/1.38 % (21685)------------------------------
% 1.66/1.38 % (21685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (21685)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (21685)Memory used [KB]: 5500
% 1.66/1.38 % (21685)Time elapsed: 0.003 s
% 1.66/1.38 % (21685)Instructions burned: 6 (million)
% 1.66/1.38 % (21685)------------------------------
% 1.66/1.38 % (21685)------------------------------
% 1.66/1.38 % (21684)Instruction limit reached!
% 1.66/1.38 % (21684)------------------------------
% 1.66/1.38 % (21684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (21684)Termination reason: Unknown
% 1.66/1.38 % (21684)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (21684)Memory used [KB]: 5500
% 1.66/1.38 % (21684)Time elapsed: 0.004 s
% 1.66/1.38 % (21684)Instructions burned: 5 (million)
% 1.66/1.38 % (21684)------------------------------
% 1.66/1.38 % (21684)------------------------------
% 1.66/1.38 % (21671)Refutation found. Thanks to Tanya!
% 1.66/1.38 % SZS status Theorem for DTF2THF_21395
% 1.66/1.38 % SZS output start Proof for DTF2THF_21395
% 1.66/1.38 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.66/1.38 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.66/1.38 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.66/1.38 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.66/1.38 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.66/1.38 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.66/1.38 thf(func_def_11, type, ph7: !>[X0: $tType]:(X0)).
% 1.66/1.38 thf(func_def_18, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.66/1.38 thf(func_def_19, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.66/1.38 thf(f430,plain,(
% 1.66/1.38 $false),
% 1.66/1.38 inference(avatar_sat_refutation,[status(thm)],[f82,f429])).
% 1.66/1.38 thf(f429,plain,(
% 1.66/1.38 spl6_2),
% 1.66/1.38 inference(avatar_contradiction_clause,[status(thm)],[f428])).
% 1.66/1.38 thf(f428,plain,(
% 1.66/1.38 $false | spl6_2),
% 1.66/1.38 inference(subsumption_resolution,[status(thm)],[f424,f44])).
% 1.66/1.38 thf(f44,plain,(
% 1.66/1.38 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2),
% 1.66/1.38 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.66/1.38 thf(f43,definition,(
% 1.66/1.38 spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 1.66/1.38 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.66/1.38 thf(f424,plain,(
% 1.66/1.38 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_2),
% 1.66/1.38 inference(equality_proxy_clausification,[status(thm)],[f423])).
% 1.66/1.38 thf(f423,plain,(
% 1.66/1.38 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.66/1.38 thf(f422,plain,(
% 1.66/1.38 ($true != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | spl6_2),
% 1.66/1.38 inference(boolean_simplification,[status(thm)],[f421])).
% 1.66/1.38 thf(f421,plain,(
% 1.66/1.38 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f420])).
% 1.66/1.38 thf(f420,plain,(
% 1.66/1.38 ($true != $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | spl6_2),
% 1.66/1.38 inference(boolean_simplification,[status(thm)],[f419])).
% 1.66/1.38 thf(f419,plain,(
% 1.66/1.38 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f418])).
% 1.66/1.38 thf(f418,plain,(
% 1.66/1.38 ($false = $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | spl6_2),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f405])).
% 1.66/1.38 thf(f405,plain,(
% 1.66/1.38 ( ! [X0 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true)) ) | spl6_2),
% 1.66/1.38 inference(superposition,[status(thm)],[f16,f312])).
% 1.66/1.38 thf(f312,plain,(
% 1.66/1.38 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f311])).
% 1.66/1.38 thf(f311,plain,(
% 1.66/1.38 ($false = $true) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.66/1.38 inference(duplicate_literal_removal,[status(thm)],[f310])).
% 1.66/1.38 thf(f310,plain,(
% 1.66/1.38 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($false = $true) | ($false = $true) | spl6_2),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f293])).
% 1.66/1.38 thf(f293,plain,(
% 1.66/1.38 ( ! [X0 : $i,X1 : $i] : (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X1) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X0) = $true)) ) | spl6_2),
% 1.66/1.38 inference(superposition,[status(thm)],[f189,f273])).
% 1.66/1.38 thf(f273,plain,(
% 1.66/1.38 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.66/1.38 thf(f272,plain,(
% 1.66/1.38 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($false = $true) | spl6_2),
% 1.66/1.38 inference(duplicate_literal_removal,[status(thm)],[f271])).
% 1.66/1.38 thf(f271,plain,(
% 1.66/1.38 ($false = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($false = $true) | spl6_2),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f264])).
% 1.66/1.38 thf(f264,plain,(
% 1.66/1.38 ( ! [X10 : $i,X9 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 1.66/1.38 inference(primitive_instantiation,[status(thm)],[f160])).
% 1.66/1.38 thf(f160,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 1.66/1.38 inference(subsumption_resolution,[status(thm)],[f152,f44])).
% 1.66/1.38 thf(f152,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true)) )),
% 1.66/1.38 inference(equality_proxy_clausification,[status(thm)],[f151])).
% 1.66/1.38 thf(f151,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true)) )),
% 1.66/1.38 inference(equality_proxy_clausification,[status(thm)],[f150])).
% 1.66/1.38 thf(f150,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.66/1.38 thf(f149,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (($true != $true) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 1.66/1.38 inference(boolean_simplification,[status(thm)],[f148])).
% 1.66/1.38 thf(f148,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : ((((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true)) )),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.66/1.38 thf(f135,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X9) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 1.66/1.38 inference(primitive_instantiation,[status(thm)],[f13])).
% 1.66/1.38 thf(f13,plain,(
% 1.66/1.38 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X9 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true) | ((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 1.66/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.38 thf(f12,plain,(
% 1.66/1.38 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) & ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) | ((((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) & ! [X8 : $i] : (((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true) | ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true)) & ! [X9 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true) | ((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true))) | ! [X10 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)))),
% 1.66/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 1.66/1.38 thf(f9,plain,(
% 1.66/1.38 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i,X3 : $i > $o] : (((X1 @ X3 @ X3 @ X2) != $true) & ((X0 @ X3 @ X3 @ X2) != $true)) => (((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) & ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)))),
% 1.66/1.38 introduced(definition,[],[choice_axiom])).
% 1.66/1.38 thf(f10,plain,(
% 1.66/1.38 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (? [X7 : $i] : (((X0 @ X4 @ X5 @ X7) != $true) & ((X1 @ X4 @ X5 @ X7) != $true)) & ! [X8 : $i] : (((X0 @ X4 @ X6 @ X8) = $true) | ((X1 @ X4 @ X6 @ X8) = $true)) & ! [X9 : $i] : (((X1 @ X6 @ X5 @ X9) = $true) | ((X0 @ X6 @ X5 @ X9) = $true))) => (? [X7 : $i] : (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) != $true) & ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) != $true)) & ! [X8 : $i] : (((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true) | ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true)) & ! [X9 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true) | ((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9) = $true))))),
% 1.66/1.38 introduced(definition,[],[choice_axiom])).
% 1.66/1.38 thf(f11,plain,(
% 1.66/1.38 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X7 : $i] : (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) != $true) & ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) != $true)) => (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 1.66/1.38 introduced(definition,[],[choice_axiom])).
% 1.66/1.38 thf(f8,plain,(
% 1.66/1.38 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i,X3 : $i > $o] : (((X1 @ X3 @ X3 @ X2) != $true) & ((X0 @ X3 @ X3 @ X2) != $true)) | ? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (? [X7 : $i] : (((X0 @ X4 @ X5 @ X7) != $true) & ((X1 @ X4 @ X5 @ X7) != $true)) & ! [X8 : $i] : (((X0 @ X4 @ X6 @ X8) = $true) | ((X1 @ X4 @ X6 @ X8) = $true)) & ! [X9 : $i] : (((X1 @ X6 @ X5 @ X9) = $true) | ((X0 @ X6 @ X5 @ X9) = $true))) | ! [X10 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)))),
% 1.66/1.38 inference(rectify,[status(thm)],[f7])).
% 1.66/1.38 thf(f7,plain,(
% 1.66/1.38 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i,X2 : $i > $o] : (((X0 @ X2 @ X2 @ X3) != $true) & ((X1 @ X2 @ X2 @ X3) != $true)) | ? [X5 : $i > $o,X6 : $i > $o,X4 : $i > $o] : (? [X9 : $i] : (((X1 @ X5 @ X6 @ X9) != $true) & ((X0 @ X5 @ X6 @ X9) != $true)) & ! [X7 : $i] : (((X1 @ X5 @ X4 @ X7) = $true) | ((X0 @ X5 @ X4 @ X7) = $true)) & ! [X8 : $i] : (((X0 @ X4 @ X6 @ X8) = $true) | ((X1 @ X4 @ X6 @ X8) = $true))) | ! [X10 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)))),
% 1.66/1.38 inference(flattening,[status(thm)],[f6])).
% 1.66/1.38 thf(f6,plain,(
% 1.66/1.38 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (? [X9 : $i] : (((X1 @ X5 @ X6 @ X9) != $true) & ((X0 @ X5 @ X6 @ X9) != $true)) & (! [X8 : $i] : (((X0 @ X4 @ X6 @ X8) = $true) | ((X1 @ X4 @ X6 @ X8) = $true)) & ! [X7 : $i] : (((X1 @ X5 @ X4 @ X7) = $true) | ((X0 @ X5 @ X4 @ X7) = $true)))) | ? [X3 : $i,X2 : $i > $o] : (((X0 @ X2 @ X2 @ X3) != $true) & ((X1 @ X2 @ X2 @ X3) != $true)) | ! [X10 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)))),
% 1.66/1.38 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.38 thf(f5,plain,(
% 1.66/1.38 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : ((! [X8 : $i] : (((X0 @ X4 @ X6 @ X8) = $true) | ((X1 @ X4 @ X6 @ X8) = $true)) & ! [X7 : $i] : (((X1 @ X5 @ X4 @ X7) = $true) | ((X0 @ X5 @ X4 @ X7) = $true))) => ! [X9 : $i] : (((X1 @ X5 @ X6 @ X9) = $true) | ((X0 @ X5 @ X6 @ X9) = $true))) & ! [X2 : $i > $o,X3 : $i] : (((X0 @ X2 @ X2 @ X3) = $true) | ((X1 @ X2 @ X2 @ X3) = $true)) & ~! [X10 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)))),
% 1.66/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.38 thf(f4,plain,(
% 1.66/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((! [X7 : $i] : ((X1 @ X5 @ X4 @ X7) | (X0 @ X5 @ X4 @ X7)) & ! [X8 : $i] : ((X1 @ X4 @ X6 @ X8) | (X0 @ X4 @ X6 @ X8))) => ! [X9 : $i] : ((X1 @ X5 @ X6 @ X9) | (X0 @ X5 @ X6 @ X9))) & ~! [X10 : $i] : ((X0 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X1 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))),
% 1.66/1.38 inference(rectify,[status(thm)],[f2])).
% 1.66/1.38 thf(f2,negated_conjecture,(
% 1.66/1.38 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X4 : $i > $o,X2 : $i > $o,X5 : $i > $o] : ((! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))),
% 1.66/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.38 thf(f1,conjecture,(
% 1.66/1.38 ? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X4 : $i > $o,X2 : $i > $o,X5 : $i > $o] : ((! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))),
% 1.66/1.38 file('/export/starexec/sandbox2/tmp/tmp.fALW8lDNi7/DTF2THF_21395.p',cTHM120D_pme)).
% 1.66/1.38 thf(f189,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 1.66/1.38 inference(subsumption_resolution,[status(thm)],[f182,f44])).
% 1.66/1.38 thf(f182,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 1.66/1.38 inference(equality_proxy_clausification,[status(thm)],[f181])).
% 1.66/1.38 thf(f181,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 1.66/1.38 inference(equality_proxy_clausification,[status(thm)],[f180])).
% 1.66/1.38 thf(f180,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.66/1.38 thf(f179,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ($true != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true)) )),
% 1.66/1.38 inference(boolean_simplification,[status(thm)],[f178])).
% 1.66/1.38 thf(f178,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true)) )),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f164])).
% 1.66/1.38 thf(f164,plain,(
% 1.66/1.38 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true)) )),
% 1.66/1.38 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.66/1.38 thf(f14,plain,(
% 1.66/1.38 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true) | ((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8) = $true)) )),
% 1.66/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.38 thf(f16,plain,(
% 1.66/1.38 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) )),
% 1.66/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.38 thf(f82,plain,(
% 1.66/1.38 ~spl6_2),
% 1.66/1.38 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.66/1.38 thf(f81,plain,(
% 1.66/1.38 $false | ~spl6_2),
% 1.66/1.38 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.66/1.38 thf(f80,plain,(
% 1.66/1.38 ($false = $true) | ~spl6_2),
% 1.66/1.38 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.66/1.38 thf(f79,plain,(
% 1.66/1.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl6_2),
% 1.66/1.38 inference(argument_congruence,[status(thm)],[f45])).
% 1.66/1.38 thf(f45,plain,(
% 1.66/1.38 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2),
% 1.66/1.38 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.66/1.38 % SZS output end Proof for DTF2THF_21395
% 1.66/1.38 % (21671)------------------------------
% 1.66/1.38 % (21671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (21671)Termination reason: Refutation
% 1.66/1.38
% 1.66/1.38 % (21671)Memory used [KB]: 6012
% 1.66/1.38 % (21671)Time elapsed: 0.057 s
% 1.66/1.38 % (21671)Instructions burned: 89 (million)
% 1.66/1.38 % (21671)------------------------------
% 1.66/1.38 % (21671)------------------------------
% 1.66/1.38 % (21665)Success in time 0.066 s
%------------------------------------------------------------------------------